3
\includegraphics[max width=\textwidth, alt={}, center]{af7d1fc8-5552-48b8-a359-895b2b5d3d6c-2_279_905_1560_621} One end of a light inextensible string of length 0.2 m is attached to a fixed point \(A\) which is above a smooth horizontal surface. A particle \(P\) of mass 0.6 kg is attached to the other end of the string. \(P\) moves in a circle on the surface with constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), with the string taut and making an angle of \(30 ^ { \circ }\) to the horizontal (see diagram).

1. Given that \(v = 1.5\), calculate the magnitude of the force that the surface exerts on \(P\).
2. Given instead that \(P\) moves with its greatest possible speed while remaining in contact with the surface, find \(v\).